%latex.default(object = result, title = "", file = paste0("tables/",     filename, ".tex"), label = paste0("tb_", type), caption = caption,     insert.bottom = note, first.hline.double = FALSE, rowname = rownames,     cgroup = c("$n = 200$", "", "$n = 1000$", "", "$n = 200$",         "", "$n = 1000$"), n.cgroup = c(2, 1, 2, 2, 2, 1, 2),     cgroupTexCmd = "", colheads = clabels, rgroup = c("Correct PS model",         "Misspecified PS model"), n.rgroup = c(rep(nrow(res1),         2)), longtable = FALSE, center = "centering")%
\begin{table}[!tbp]
\caption{Simulation results: Exponential outcome model 2\label{tb_exp2}} 
{\centering
\begin{tabular}{lrrcrcrrcrrcrrcrcrr}
\hline
\multicolumn{1}{l}{\ }&\multicolumn{2}{c}{\ $n = 200$}&\multicolumn{1}{c}{\ }&\multicolumn{1}{c}{\ }&\multicolumn{1}{c}{\ }&\multicolumn{2}{c}{\ $n = 1000$}&\multicolumn{1}{c}{\ }&\multicolumn{2}{c}{\ }&\multicolumn{1}{c}{\ }&\multicolumn{2}{c}{\ $n = 200$}&\multicolumn{1}{c}{\ }&\multicolumn{1}{c}{\ }&\multicolumn{1}{c}{\ }&\multicolumn{2}{c}{\ $n = 1000$}\tabularnewline
\cline{2-3} \cline{7-8} \cline{13-14} \cline{18-19}
\multicolumn{1}{l}{}&\multicolumn{1}{c}{Bias}&\multicolumn{1}{c}{RMSE}&\multicolumn{1}{c}{}&\multicolumn{1}{c}{}&\multicolumn{1}{c}{}&\multicolumn{1}{c}{Bias}&\multicolumn{1}{c}{RMSE}&\multicolumn{1}{c}{}&\multicolumn{1}{c}{}&\multicolumn{1}{c}{}&\multicolumn{1}{c}{}&\multicolumn{1}{c}{Bias}&\multicolumn{1}{c}{RMSE}&\multicolumn{1}{c}{}&\multicolumn{1}{c}{}&\multicolumn{1}{c}{}&\multicolumn{1}{c}{Bias}&\multicolumn{1}{c}{RMSE}\tabularnewline
\hline
{\bfseries Correct PS model}&&&&&&&&&&&&&&&&&&\tabularnewline
~~\textbf{nDBW}&$-1.07$&$ 10.63$&&$$&&$-0.38$&$  4.98$&&$$&$$&&$ -3.95$&$11.52$&&$$&&$ -1.03$&$ 5.34$\tabularnewline
~~MLE&$-1.29$&$ 22.02$&&$$&&$-0.17$&$  9.15$&&$$&$$&&$ -0.89$&$31.26$&&$$&&$  0.23$&$14.07$\tabularnewline
~~CBPS&$ 2.04$&$ 12.17$&&$$&&$ 0.39$&$  5.46$&&$$&$$&&$  2.08$&$13.63$&&$$&&$  0.37$&$ 6.59$\tabularnewline
~~Calibrated weighting&$-1.76$&$ 10.55$&&$$&&$-0.41$&$  4.90$&&$$&$$&&$ -2.50$&$11.56$&&$$&&$ -0.68$&$ 5.71$\tabularnewline
~~Entropy balancing&$-5.84$&$ 11.51$&&$$&&$-4.81$&$  6.59$&&$$&$$&&$ -5.76$&$12.05$&&$$&&$ -4.75$&$ 6.83$\tabularnewline
~~True propensity score&$-0.84$&$ 39.62$&&$$&&$ 0.41$&$ 18.13$&&$$&$$&&$ -0.93$&$48.77$&&$$&&$ -0.28$&$22.09$\tabularnewline
~~Unweighted&$14.03$&$ 18.73$&&$$&&$14.34$&$ 15.41$&&$$&$$&&$-14.39$&$18.03$&&$$&&$-14.31$&$15.13$\tabularnewline
~~\textbf{nDBW DR}&$-2.85$&$ 11.43$&&$$&&$-0.77$&$  5.09$&&$$&$$&&$ -5.32$&$12.05$&&$$&&$ -1.41$&$ 5.48$\tabularnewline
~~MLE DR&$-1.91$&$ 14.22$&&$$&&$-0.20$&$  6.55$&&$$&$$&&$ -2.77$&$17.88$&&$$&&$ -0.33$&$ 9.64$\tabularnewline
~~CBPS DR&$-2.35$&$ 12.78$&&$$&&$-0.42$&$  6.00$&&$$&$$&&$ -3.17$&$13.59$&&$$&&$ -0.69$&$ 7.28$\tabularnewline
~~Calibrated weighting DR&$-2.67$&$ 11.79$&&$$&&$-0.60$&$  5.40$&&$$&$$&&$ -3.78$&$12.00$&&$$&&$ -1.00$&$ 5.95$\tabularnewline
~~Entropy balancing DR&$-7.04$&$ 13.28$&&$$&&$-5.60$&$  7.53$&&$$&$$&&$ -8.70$&$13.92$&&$$&&$ -6.93$&$ 8.60$\tabularnewline
~~True propensity score DR~~&$-2.06$&$ 14.14$&&$$&&$-0.31$&$  6.79$&&$$&$$&&$ -3.27$&$19.39$&&$$&&$ -0.55$&$10.54$\tabularnewline
~~Imputation&$-0.70$&$ 13.16$&&$$&&$ 0.68$&$  5.98$&&$$&$$&&$-20.27$&$22.67$&&$$&&$-19.85$&$20.36$\tabularnewline
\hline
{\bfseries Misspecified PS model}&&&&&&&&&&&&&&&&&&\tabularnewline
~~\textbf{nDBW}&$10.55$&$ 17.32$&&$$&&$11.99$&$ 13.47$&&$$&$$&&$-12.99$&$16.97$&&$$&&$ -7.26$&$ 8.89$\tabularnewline
~~MLE&$33.66$&$145.54$&&$$&&$60.81$&$362.53$&&$$&$$&&$-18.59$&$27.04$&&$$&&$-18.18$&$19.73$\tabularnewline
~~CBPS&$12.17$&$ 19.73$&&$$&&$ 7.11$&$  9.72$&&$$&$$&&$ -9.60$&$16.34$&&$$&&$-15.25$&$16.43$\tabularnewline
~~Calibrated weighting&$ 8.63$&$ 16.01$&&$$&&$10.26$&$ 11.93$&&$$&$$&&$-11.35$&$15.56$&&$$&&$ -9.81$&$11.04$\tabularnewline
~~Entropy balancing&$ 4.84$&$ 14.05$&&$$&&$ 6.36$&$  8.68$&&$$&$$&&$-16.36$&$19.28$&&$$&&$-15.34$&$16.07$\tabularnewline
~~True propensity score&$ 0.72$&$ 39.87$&&$$&&$-0.68$&$ 17.44$&&$$&$$&&$  0.49$&$50.87$&&$$&&$  0.20$&$22.79$\tabularnewline
~~Unweighted&$14.67$&$ 19.55$&&$$&&$14.42$&$ 15.51$&&$$&$$&&$-14.46$&$18.11$&&$$&&$-14.24$&$15.12$\tabularnewline
~~\textbf{nDBW DR}&$ 7.97$&$ 15.57$&&$$&&$ 9.73$&$ 11.41$&&$$&$$&&$-11.74$&$15.76$&&$$&&$ -8.50$&$ 9.80$\tabularnewline
~~MLE DR&$20.04$&$ 59.54$&&$$&&$49.55$&$355.21$&&$$&$$&&$-13.17$&$18.47$&&$$&&$-12.22$&$13.54$\tabularnewline
~~CBPS DR/BRDR&$10.71$&$ 18.34$&&$$&&$13.09$&$ 14.81$&&$$&$$&&$-13.05$&$17.38$&&$$&&$-12.94$&$14.02$\tabularnewline
~~Calibrated weighting DR&$ 8.62$&$ 16.01$&&$$&&$10.26$&$ 11.93$&&$$&$$&&$-11.35$&$15.56$&&$$&&$ -9.81$&$11.04$\tabularnewline
~~Entropy balancing DR&$ 4.84$&$ 14.05$&&$$&&$ 6.36$&$  8.68$&&$$&$$&&$-16.36$&$19.28$&&$$&&$-15.34$&$16.07$\tabularnewline
~~True propensity score DR~~&$-1.59$&$ 14.40$&&$$&&$-0.43$&$  6.71$&&$$&$$&&$ -3.20$&$19.84$&&$$&&$ -0.49$&$10.52$\tabularnewline
~~Imputation&$-0.41$&$ 13.51$&&$$&&$ 0.78$&$  5.98$&&$$&$$&&$-20.46$&$22.83$&&$$&&$-19.83$&$20.37$\tabularnewline
\hline
\end{tabular}}
\parbox{0.99\textwidth}
		{Notes: This simulation compares the performance of various methods 
		for estimating propensity scores and (inverse probability) weights 
		by investigating combinations of six versions of the true outcome model 
		(linear~1, linear~2, quadratic~1, quadratic~2, exponential~1, and exponential~2)
		and two versions of coefficients for the true propensity score model (type~A and B)
		with the two different numbers of observations ($n = 200$ and $n = 1000$).
		For each estimation method, I use two propensity score model specifications 
		(correct and misspecified) and report the bias and RMSE for each in the table.}\end{table}
